I'm sure there are lots of questions here about making up words. We can't help you with your name — that's off-topic — but it's possible to comment on how to create one.
If you need a particular word, you need that particular word. You might get away with a misspelling which results in a similar sound, like
place4bizness.com, provided that it cannot be misread.
In that example, the different words are distinguished by including a digit 4 for the word for, and business is deliberately misspelled both to shorten it and perhaps make it more memorable. But bizness is pronounced the same as business, and it's not similar to any other word; it's not likely to be misread.
When writing such names, you can use capital letters, or differentiate using typeface. For a slightly worse example, placeforbusiness.com, PlaceForBusiness.com and placeforbusiness.com are all valid. Domain names standardise on lower-case letters, but part of the standard is that they are not case-sensitive and capital letters map on to the corresponding lower-case letter.
Using a double t as you suggest is likely to be misread, because partty is not a word and parity is.